Let

f(x, y, z) = z tan? 1(y2)i + z3 ln(x2 + 7)j + zk.

find the flux of f across s, the part of the paraboloid

x2 + y2 + z = 27

that lies above the plane

z = 2

and is oriented upward.

\int \int_{s}^{} f*ds

has divergence

If includes the disk which is contained in the paraboloid, then by the divergence theorem the flux is

If the disk is not part of , then subtract the flux of across the disk (with downward orientation; call it ). Parameterize by

where and , with normal vector

Then the flux of across is

which makes the flux across , .

i did it myself and i got 4.2 (b) hope its right

step-by-step explanation:

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2